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Summary: State-Dependent Representation Independence
(Technical Appendix)
Amal Ahmed Derek Dreyer Andreas Rossberg
TTI-C MPI-SWS MPI-SWS
amal@tti-c.org dreyer@mpi-sws.mpg.de rossberg@mpi-sws.mpg.de
August 4, 2008
Contents
1 The Language Fµ!
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1.1 Syntax, Dynamic Semantics and Static Semantics . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Contexts and Contextual Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Step-Indexed Logical Relation for Fµ!
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3 Logical Relation Proofs 15
3.1 Basic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.1 Properties of Step-Indexed Construction . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.2 Approximation Yields Valid Semantic Objects . . . . . . . . . . . . . . . . . . . . . . 17
3.1.3 World Extension and Store Satisfaction Properties . . . . . . . . . . . . . . . . . . . . 18
3.1.4 Validity of Type Interpretations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.5 Substitution Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
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